Finite Group Databasebeta

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C4×C23×C41⋊C5 #34038188

order18860
automorphism?
homologyAbelianization (H1) = C4×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC4×C23×C41⋊C5
unambiguous semidirect product(C4×C41)⋊(C5×C23)
unambiguous semidirect product(C4×C23×C41)⋊C5

Splittings

Fitting, HallC4×C23×C41 ⋊ C5
derived, SylowC41 ⋊ C4×C5×C23
HallC23×C41 ⋊ C4×C5
HallC4×C41 ⋊ C5×C23

Subgroups

subgroupG/H
center, hypercenterC4×C23C41⋊C5
commutator, hypocenterC41C4×C5×C23
FrattiniC2C2×C23×C41⋊C5
FittingC4×C23×C41C5
socleC2×C23×C41C2×C5
prime radicalC2×C23×C41⋊C5C2
cosocleC2×C41C2×C5×C23
LCSG ▷ C41
UCSC1 ◁ C4×C23

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3772

Conjugacy classes & character table

1196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18860, 2);